this is known as a uniform spanning tree https://en.wikipedia.org/wiki/Spanning_...

this is known as a uniform spanning tree https://en.wikipedia.org/wiki/Spanning_tree

these can be sampled using Wilson's algorithm for Loop-Erased Random Walks https://en.wikipedia.org/wiki/Loop-erased_random_walk#The_un...

Here is a nice visualization of Wilson's algorithm using d3.js by Michael Bostock (NY Times) http://bl.ocks.org/mbostock/11357811

9ac345a5509a on July 10, 2015 [–]

The number of such mazes is also on OEIS under A007341: http://oeis.org/A007341